This is a phase-modulated continuous-wave (PMCW) radar simulation example based on RadarSimPy.
RadarSimPyis a radar simulation package built with python. Contact me if you are interested in this module.
This notebook is available on my GitHub.
The following table lists the basic parameters of the radar transmitter.
| Parameter | Variable in RadarSimPy |
Value |
|---|---|---|
| Center frequency ($f_c$) | fc | 24.125 GHz |
| Bandwidth ($B$) | bandwidth | 0 Hz |
| Transmitted power ($P_t$) | tx_power | 20 dBm |
| Pulse repetition period | repetition_period | 2.1 us |
| Pulse length ($T$) | pulse_length | 2.1 us |
| Number of pulses | pulses | 256 |
The transmitted signals are modulated with phase codes. The length of the phase code is 255 with the code rate of 256 Mb/s.
The parameters of the receiver are listed in the table below.
| Parameter | Variable in RadarSimPy |
Value |
|---|---|---|
| Sampling rate ($f_s$) | fs | 250 Msps |
| Noise figure ($NF$) | noise_figure | 10 dB |
| RF gain/loss ($G_{rf}$) | rf_gain | 20 dB |
| Load resistor ($R_L$) | load_resistor | 1000 $\Omega$ |
| Baseband voltage gain ($G_{BB}$) | baseband_gain | 30 dB |
import numpy as np
from radarsimpy import Radar, Transmitter, Receiver
angle = np.arange(-90, 91, 1)
pattern = 20 * np.log10(np.cos(angle / 180 * np.pi) + 0.01) + 12
code1 = np.array([1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1,
1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1,
1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1,
-1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1,
1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1,
1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1,
1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1,
-1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1,
-1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1,
1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1,
1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1,
-1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1,
-1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1,
-1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1,
1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1,
1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1])
code2 = np.array([1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1,
-1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1,
-1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1,
-1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1,
1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1,
-1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1,
1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1,
1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1,
-1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1,
-1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1,
1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1,
1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1,
-1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1,
-1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1,
1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1,
-1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1])
phase_code1=np.zeros(np.shape(code1))
phase_code2=np.zeros(np.shape(code2))
phase_code1[np.where(code1 == 1)] = 0
phase_code1[np.where(code1 == -1)] = 180
phase_code2[np.where(code2 == 1)] = 0
phase_code2[np.where(code2 == -1)] = 180
tx_channel_1 = dict(
location=(0, 0, 0),
azimuth_angle=angle,
azimuth_pattern=pattern,
elevation_angle=angle,
elevation_pattern=pattern,
chip_length=4e-9,
phase_code=phase_code1,
)
tx_channel_2 = dict(
location=(0, 0, 0),
azimuth_angle=angle,
azimuth_pattern=pattern,
elevation_angle=angle,
elevation_pattern=pattern,
chip_length=4e-9,
phase_code=phase_code2,
delay=0.01
)
tx = Transmitter(fc=24.125e9,
tx_power=20,
pulses=256,
pulse_length=2.1e-6,
channels=[tx_channel_1, tx_channel_2])
rx = Receiver(fs=250e6,
noise_figure=10,
rf_gain=20,
baseband_gain=30,
load_resistor=1000,
channels=[
dict(location=(0, 0, 0),
azimuth_angle=angle,
azimuth_pattern=pattern,
elevation_angle=angle,
elevation_pattern=pattern)
])
Create the FMCW radar model based on all the parameters defined above.
radar = Radar(transmitter=tx, receiver=rx)
The propertities of targets are defined here. There are 3 targets in this simulation. The locations of the targets are defined through $(x, y, z)$ coordinates in meters, and the speeds of the targets are defined trough $(v_x, v_y, v_z)$ in $m/s$. The propertites of the targets also includes radar cross-section (RCS (dBsm)) and phase (radian).
target_1 = dict(location=(20, 0, 0),
speed=(-200, 0, 0),
rcs=20,
phase=0)
target_2 = dict(location=(70, 0, 0),
speed=(0, 0, 0),
rcs=35,
phase=0)
target_3 = dict(location=(33, 10, 0),
speed=(100, 0, 0),
rcs=20,
phase=0)
targets = [target_1, target_2, target_3]
from radarsimpy import simulator as sim
data = sim(radar, targets, noise=True)
time_matrix = data['timestamp']
data_matrix = data['baseband']
%timeit sim(radar, targets)
8.63 s ± 1.22 s per loop (mean ± std. dev. of 7 runs, 1 loop each)
from radarsimpy import simulatorcpp as simcpp
datacpp = simcpp(radar, targets, noise=True)
time_matrixcpp = datacpp['timestamp']
data_matrixcpp = datacpp['baseband']
%timeit simcpp(radar, targets)
624 ms ± 38.5 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
Plot
import plotly.graph_objs as go
from plotly.offline import iplot
beat_I = go.Scatter(
x=time_matrixcpp[0, 0, :],
y=np.real(data_matrixcpp[1, 255, :]),
name='I',
)
beat_Q = go.Scatter(
x=time_matrixcpp[0, 0, :],
y=np.imag(data_matrixcpp[1, 255, :]),
name='Q',
)
data = [beat_I, beat_Q]
layout = go.Layout(
title='I/Q Baseband Signals',
yaxis=dict(title='Amplitude (V)'),
xaxis=dict(title='Time (s)'),
)
fig = go.Figure(data, layout=layout)
iplot(fig)
code_length = 255
range_profile = np.zeros(
(radar.channel_size, radar.transmitter.pulses, code_length), dtype=complex)
for pulse_idx in range(0, radar.transmitter.pulses):
for bin_idx in range(0, code_length):
range_profile[:, pulse_idx, bin_idx] = np.sum(
code2*data_matrixcpp[1, pulse_idx, bin_idx:(bin_idx+code_length)])
bin_size = 3e8/2*4e-9
range_bin = np.arange(0, code_length, 1)*bin_size
Plot
temp = np.abs(range_profile[1, :, :])
temp = 20 * np.log10(temp + 0.001)
range_axis = np.arange(0, code_length, 1)*bin_size
doppler_axis = np.linspace(
0, radar.transmitter.pulses, radar.transmitter.pulses, endpoint=False)
data = [go.Surface(x=range_axis, y=doppler_axis, z=temp, colorscale='Rainbow')]
layout = go.Layout(
title='Range Profile',
height=800,
scene=dict(
xaxis=dict(title='Range (m)'),
yaxis=dict(title='Chirp'),
zaxis=dict(title='Amplitude (dB)'),
aspectmode='cube',
),
margin=dict(l=0, r=0, b=60, t=100),
legend=dict(orientation='h'),
)
fig = go.Figure(data=data, layout=layout)
iplot(fig)
from scipy import signal
doppler_window = signal.chebwin(radar.transmitter.pulses, at=50)
range_doppler = np.zeros(np.shape(range_profile), dtype=complex)
for ii in range(0, radar.channel_size):
for jj in range(0, code_length):
range_doppler[ii, :, jj] = np.fft.fftshift(np.fft.fft(
range_profile[ii, :, jj] * doppler_window,
n=radar.transmitter.pulses,
))
unambiguous_speed = 3e8 / radar.transmitter.repetition_period / radar.transmitter.fc / 2
temp = np.abs(range_doppler[1, :, :])
temp = 20 * np.log10(temp)
range_axis = np.arange(0, code_length, 1)*bin_size
doppler_axis = np.linspace(
-unambiguous_speed/2, unambiguous_speed/2, radar.transmitter.pulses, endpoint=False)
data = [go.Surface(x=range_axis, y=doppler_axis, z=temp, colorscale='Rainbow')]
layout = go.Layout(
title='Range Doppler',
height=800,
scene=dict(
xaxis=dict(title='Range (m)'),
yaxis=dict(title='Velocity (m/s)'),
zaxis=dict(title='Amplitude (dB)'),
aspectmode='cube',
),
margin=dict(l=0, r=0, b=60, t=100),
legend=dict(orientation='h'),
)
fig = go.Figure(data=data, layout=layout)
iplot(fig)